Anastomosis is the joining of two vessels together to establish fluid communication between them. One approach to accomplish this coupling has been to provide a surgical instrument having a clamp carrying a fastener. In such instruments the clamp generally has two members, each carrying a portion of the fastener that pivots towards each other to close the fastener. In many embodiments, each portion of the fastener includes a ring having axially directed pins and corresponding pin receiving holes. Such an approach to anastomosis has been described in Applicant's own U.S. Pat. Nos. 4,607,637, 4,624,257, 4,917,090, and 4,917,091, the disclosures of which are hereby incorporated by reference. Unfortunately, as the ring and/or pin size increases it becomes more difficult to align the pins with their corresponding holes on the opposite fastener piece because of the angles produced in the pivoting closure movement. This restriction can result in the use of smaller than optimum ring sizes and/or larger tools that are cumbersome in a surgical area.